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This paper presents a probabilistic approach in the modeling of stand-alone microgrids to predict their operational adequacy performance considering uncertainty of energy storage system (ESS), photovoltaic system (PVS) and conventional generator (CG). Instead of using the daily or hourly time step, operating period a minutely time step is considered to incorporate the effect of fast ramp up/down of system components on microgrid operating adequacy through expected energy not supplied (EENS) and expected energy not used (EENU), due to load and resource variations. A time varying state of charge (SOC) model is proposed to determine power output of an ESS in reliability modeling. The reliability of a PVS is modeled in detail based on the total cross-tied configuration (TCTC) of photovoltaic (PV) cells and arrays. The proposed technique and indices will be useful for system planners to select the type and size of microgrid systems that contain alternative energy sources and storage. [ABSTRACT FROM PUBLISHER]

The Newton-Raphson (NR) method is a powerful tool in nonlinear equations. However, a well-known disadvantage of this method is that the initial iteration value must be chosen sufficiently close to a true solution in order to guarantee its convergence. The Kantorovich theorem is virtually the only known sufficiency condition for convergence of NR method, and gives very conservative bounds. This letter analyzes the convergence of the NR method in feasible power-flow for direct-current (DC) network, and an explicit convergence condition is obtained. Comparing with the existing results, the proposed convergence condition is more concise and less conservative. Moreover, according to the proposed condition, one can easily set the initial iteration value to guarantee the convergence of the NR method. Case studies verify the correctness of the presented analysis. [ABSTRACT FROM AUTHOR]